The thumbs are our strongest and most versatile fingers, yet they are only used for adding spaces in most standard keyboards, apparently as a some kind of a strange typewriter-era relic. Thumb-o-Board is here to fix that - the shift for example is placed under the default resting position of your left thumb.

As you don't have to reach keys (especially the shifts) with your pinkies, the movement of your wrists is quite considerably reduced, making it faster and more ergonomic to type. All other navigation/modifier keys are accessed with the thumbs as well - a huge benefit for the frequent backspace or page up/down users for example.

Punctuation has been moved to the sides of the alphabetical keys - caps lock is replaced with comma.

The keys that have been removed:

Caps lock, num lock, scroll lock, pause, insert, print screen:
After 10 years as a windows user, I still don't understand the purpose of num lock, other than that it annoyingly locks the num pad in some computers by default. Only caps lock has managed to survive in modern mac keyboards.

F-keys:
These have become kind of useless since the invention of the mouse. While they do provide some nice workspace changes in some pro applications among other things, there's no use for them most of the time. If system-wide funtions are assigned to them, they'll interfere with the application-specific shortcuts. And since the shortcuts are almost never used consistently through different applications, they are hard to learn in the first place. Instead the Thumb-o-Board 2000 contains 6 programmable keys. If needed, F-key like functionabty could be assigned to shift + numpad for example.

Windows keys (or ctrls in mac), alt gr:
I think the windows keys were some kind of a sick scheme by Microsoft to get all 3rd party hardware marked with their logo, but they just forgot to add any functionality to the keys. Other than messing up full screen programs. Controls in macs are just as useless - they are only used for some special text manipulation/navigation functions not needed by the average user. Windows's alt gr could be replaced with just alt in many cases, or alt+ shift for example. In any case, three modifier keys is just enough.

The two deletes and backspace:
Have been merged into a single key.

Home and end:
Can be replaced with shift+page up/down for example. Or just simply by tapping either page button.

Numbers on the upper row:
It's more comfortable to input numbers using the numpad, and since the numpad is quite close to the default resting position of the hands in this layout, the upper row contains only special/punctuation characters.

81 keys in total - compared to ~104 in the standard

Improvements in ergonomics:

Special keys and numpad are easy to reach

Your hands are placed a bit more apart than in most standard keyboards

The rows of keys are aligned evenly - less finger travel and a more relaxed writing position

Almost all punctuation can be done without shifts

Colon and comma remapped to the home row

Easy to add accents, umlauts etc

The alphabetical layout featured is a slightly modified Capewell Close Keys 0.9.3 for English. At the moment I find it to be the best out of Arensito/Colemak/Capewell trio. It is however a work in progress, so the layout may change dramatically before it is officially released.
(My modifications: K moved to J's old place, J to the bottom row under the right hands ring finger, added international characters to the places of punctuation marks)

Ergonomically, the thumb buttons look like a royal pain. Because of the placement of the of the topmost thumb buttons, you would have to curl your thumb all the way under your hands or do a weird twist, disrupting the flow of typing and slowing pace even more than where the alt button already is. I like the idea of giving the thumbs more work than the usual but I think this is the wrong way to go about it. The only other thing is the switching of the punctuation and the numbers. I use punctuation a lot more than numbers and it doesn't make since to put the the punctuation further out of reach. These are just my opinions of course, and to each man his own.

I tried to find the best positions for the thumb buttons by printing the layout in "life size" and simply experimenting what felt the most comfortable to use over a longer period… The alt position is actually quite close to where I'd rest my thumbs on a standard keyboard. But I agree that they could be placed a lot better, others may find it really painful to use it like this.

But I have to disagree with what you said about the punctuation. Take the new colon position for example: Moving the pinkies to the sides of the home row requires much less effort than moving them to the bottom row. The latter makes you do this grabbing-like motion with all fingers involved, a serious flow-breaker, while the way they are placed here requires only a small wrist movement, and all other fingers remain on their home row positions. So yes, I did move the semicolon and apostrophe a bit further, but all the other punctuation should be easier to reach.